On the covariant Hamilton-Jacobi formulation of Maxwell's equations via the polysymplectic reduction

TL;DR

This paper develops a covariant Hamilton-Jacobi formulation for Maxwell's equations using a first-order Lagrangian and polysymplectic reduction within the De Donder-Weyl formalism, providing a geometric approach to classical electromagnetism.

Contribution

It introduces a novel covariant Hamilton-Jacobi framework for Maxwell's equations derived from a Palatini-like Lagrangian and polysymplectic reduction, advancing geometric formulations in field theory.

Findings

Derived a covariant Hamilton-Jacobi equation for Maxwell's equations

Applied polysymplectic reduction to the De Donder-Weyl formalism

Provided a geometric perspective on classical electromagnetism

Abstract

The covariant Hamilton-Jacobi formulation of Maxwell's equations is derived from the first-order (Palatini-like) Lagrangian using the analysis of constraints within the De~Donder-Weyl covariant Hamiltonian formalism and the corresponding polysymplectic reduction.